For part a I took the limit as x tends to zero from the right of 2x+a^2. I put zero in for x and then said a=0 which would also make the limit as x approaches zero from the left of x^2+a 0 so the function would be continuous.

There is more than one value of a that will make the function continuous at x=0, since at x=0,
x^2+a =2x+a^2
or setting x=0,
a-a²=0
a(1-a)=0
giving
a=0 or a=1.

Now you can continue with the last part.

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